Since you asked, I think the 34T freewheel is a good idea, if you've got hills to climb, and your derailleur can candle it fine, as you said. Fifteen years is getting up on old age for tires, but I've got some 25+ that are OK, but I'm careful on them (no fast descending). Also fifteen years is a good long time between lube jobs, even if it was done correctly and stored carefully, so it would be a good idea to repack the hubs and bottom bracket. The brake levers you have now are better than original, so keep them unless you decide to actually restore the bike, rather than just make it into a nice daily rider.

That's a nice bike; I hope you put a lot of miles on it.